The chairman of the Republican National Committee told a gathering of the nation’s Latino public officials Saturday that the GOP has done a “lousy” job reaching out to their community, but pledged that a new outreach campaign shows “we want to earn your trust, and your vote.”

RNC Chairman Reince Priebus also reiterated his belief in the need for “comprehensive” immigration reform but acknowledged he’s not a policy maker who can shape a plan for Republicans who control the House.

Priebus’ appearance before the National Association of Latino Elected and Appointed Officials, holding its 30th annual convention at a downtown Chicago hotel, marked another step in the GOP’s outreach efforts following an intensive study in the aftermath of the 2012 elections.

The visit also capped a week in which the Democratic-led Senate voted 68-32, with 14 Republicans in favor, for a comprehensive immigration plan that would increase border security while providing an eventual pathway to citizenship for undocumented immigrants who meet certain conditions.

Priebus, who first called for a comprehensive immigration reform plan in March, called his appearance before NALEO to discuss the subject “pretty historic.”

Still, House Republicans have said they will not take up the Senate-passed measure and will adopt a more deliberative, likely piecemeal approach. Illinois Sen. Dick Durbin, a Democratic member of the so-called Gang of Eight bipartisan senators who agreed to the plan, said a piece-by-piece vote won’t work.

“The step by step approach will never work. We tried it for years,” said Durbin, reflecting concerns that some House Republicans will scrap provisions that would grant citizenship to qualified undocumented immigrants after 13 years.

Durbin, who appeared at the conference along with Chicago Democratic Rep. Luis Gutierrez, said Republican House Speaker John Boehner should move off his pledge not to call a vote on any plan unless it has the support of a majority of GOP members. Democrats contend the Senate measure would pass the House with the votes of a unified minority Democratic caucus and pick up GOP votes.

Speaking at a luncheon of several hundred people, Priebus said “even a casual observer” could see that there is “growing diversity” in the GOP.

“I’ll be honest here. In the past two years, we’ve done a pretty lousy job of connecting in the Latino community. We’ve missed out on opportunities to build better relationships. But that’s going to change. We want to be a party that is more welcoming, more inclusive, more open,” said Priebus, who is from Kenosha, Wis.

Priebus credited the work of Florida Sen. Marco Rubio on the Gang of Eight’s immigration plan as demonstrating that Republicans are taking the lead on the issue. But a Democratic official said President Barack Obama’s decision to campaign on immigration reform was the only reason the issue has come before Congress.

Henry Munoz III of Texas, a major Obama Latino fundraiser who is the finance chairman of the Democratic National Committee, also recited a litany of presidential initiatives, ranging from his signature healthcare measure to increased grant funding for college students, as a demonstration of support for Latinos.

“I’m not here today because of any autopsy of the Democratic Party,” Munoz said. “Our outreach and engagement is not a newfound phenomenon. This isn’t the old Democratic Party or the new Democratic Party. We’re just here to continue to earn your trust.”